It is desirable to maximize the open air or open roof space above a vehicle passenger compartment, and it is common to employ a convertible system including a roof which is movable from a closed condition above the passenger compartment to a stowed (open air) condition. When a convertible roof cycles from the closed condition to the stowed condition, a main link of a linkage can swing through a portion of a headliner secured to an underside of the convertible roof. Currently, there are mechanisms which pull the fabric of the headliner out of the path of the main link as the convertible roof is moved to the stowed condition. However, these known mechanisms typically require the convertible roof to have a multi-bow construction instead of a solid frame construction.